Analysis of zz-www.sudokuwiki.org-0048-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=48
level: medium
position: ..6...5...3.2...9.1....7.36..27...6.6..5.1..2.1...67..89.1....4.6...8.7...4...8.. initial
Autosolve
position: ..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B3: 5,8 => CTR => B3: 2,4 * CNT 1 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B3: 5,8 => CTR => B3: 2,4 * DIS B3: 2,4 # H1: 8 => CTR => H1: 2,4 * DIS B3: 2,4 + H1: 2,4 # H6: 5 => CTR => H6: 4,8 * DIS B3: 2,4 + H1: 2,4 + H6: 4,8 # E5: 4,8 => CTR => E5: 3,9 * DIS B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 7 => CTR => B5: 4,8 * PRF B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 # D1: 4,8 => SOL * STA B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 + D1: 4,8 * CNT 6 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6...5...3.2...9.1....7.36..27...6.6..5.1..2.1...67..89.1....4.6...8.7...4...8.. | initial |
| ..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81. | autosolve |
| 946813527735264198128957436452789361687531942319426785893172654561348279274695813 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) F2: 4,5 I1: 7,8 G2: 1,4 G3: 2,4 H5: 4,8 H7: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I2: 1.. / G2 = 1 => 7 pairs (_) / I2 = 1 => 16 pairs (_) G4,I4: 1.. / G4 = 1 => 16 pairs (_) / I4 = 1 => 7 pairs (_) G2,G4: 1.. / G2 = 1 => 7 pairs (_) / G4 = 1 => 16 pairs (_) I2,I4: 1.. / I2 = 1 => 16 pairs (_) / I4 = 1 => 7 pairs (_) H1,G3: 2.. / H1 = 2 => 17 pairs (_) / G3 = 2 => 8 pairs (_) F7,F9: 2.. / F7 = 2 => 17 pairs (_) / F9 = 2 => 8 pairs (_) H7,G8: 2.. / H7 = 2 => 8 pairs (_) / G8 = 2 => 17 pairs (_) B3,G3: 2.. / B3 = 2 => 17 pairs (_) / G3 = 2 => 8 pairs (_) F7,H7: 2.. / F7 = 2 => 17 pairs (_) / H7 = 2 => 8 pairs (_) A8,G8: 2.. / A8 = 2 => 8 pairs (_) / G8 = 2 => 17 pairs (_) G3,G8: 2.. / G3 = 2 => 8 pairs (_) / G8 = 2 => 17 pairs (_) H1,H7: 2.. / H1 = 2 => 17 pairs (_) / H7 = 2 => 8 pairs (_) D1,F1: 3.. / D1 = 3 => 9 pairs (_) / F1 = 3 => 10 pairs (_) D8,E8: 4.. / D8 = 4 => 7 pairs (_) / E8 = 4 => 7 pairs (_) F2,E3: 5.. / F2 = 5 => 8 pairs (_) / E3 = 5 => 13 pairs (_) H6,H7: 5.. / H6 = 5 => 8 pairs (_) / H7 = 5 => 17 pairs (_) I1,I2: 7.. / I1 = 7 => 6 pairs (_) / I2 = 7 => 8 pairs (_) B5,C5: 7.. / B5 = 7 => 7 pairs (_) / C5 = 7 => 11 pairs (_) E7,E9: 7.. / E7 = 7 => 7 pairs (_) / E9 = 7 => 10 pairs (_) C7,E7: 7.. / C7 = 7 => 10 pairs (_) / E7 = 7 => 7 pairs (_) C2,I2: 8.. / C2 = 8 => 8 pairs (_) / I2 = 8 => 6 pairs (_) A1,C3: 9.. / A1 = 9 => 9 pairs (_) / C3 = 9 => 9 pairs (_) * DURATION: 0:00:27.377512 START: 04:22:36.930729 END: 04:23:04.308241 2017-05-01 * CP COUNT: (22) * INCONCLUSIVE -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F2,G2,G3,H5,H7,I1) * ..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81. * PAIR F2: 4,5 BLK 2 E3: 4,5,8,9 # reduction candidate for 4,5 E3: 8,9 # 9 pairs E3: 4,5 # 9 pairs * PAIR F2: 4,5 ROW 2 A2: 4,5,7 # reduction candidate for 4,5 A2: 4,5 # 9 pairs A2: 7 # 7 pairs * PAIR I1: 7,8 BLK 3 I2: 7,8,1 # reduction candidate for 7,8 I2: 1 # 16 pairs I2: 7,8 # 7 pairs * PAIR I1: 7,8 ROW 1 B1: 7,8,2,4 # reduction candidate for 7,8 B1: 7,8 # 9 pairs B1: 2,4 # 7 pairs * PAIR G2: 1,4 COL G G4: 1,4,3,9 # reduction candidate for 1,4 G4: 1,4 # 10 pairs G4: 3,9 # 8 pairs * PAIR G3: 2,4 BLK 3 H1: 2,4,8 # reduction candidate for 2,4 H1: 8 # 16 pairs H1: 2,4 # 7 pairs * PAIR G3: 2,4 ROW 3 B3: 2,4,5,8 # reduction candidate for 2,4 B3: 5,8 => CTR * .26.1.5...3.26..9.1....7236..27...6.6..5.1..2.1..2675.89.1..624261..8.7...46.281. B3: 2,4 # 8 pairs * PAIR H5: 4,8 BLK 6 H6: 4,8,5 # reduction candidate for 4,8 H6: 4,8 # 17 pairs H6: 5 # 8 pairs * PAIR H5: 4,8 ROW 5 B5: 4,8,7 # reduction candidate for 4,8 B5: 4,8 # 11 pairs E5: 4,8,3,9 # reduction candidate for 4,8 E5: 4,8 # 10 pairs * PAIR H5: 4,8 COL H H1: 4,8,2 # reduction candidate for 4,8 H1: 2 # 17 pairs H1: 4,8 # 8 pairs * PAIR H7: 2,5 ROW 7 F7: 2,5,3 # reduction candidate for 2,5 F7: 3 # 19 pairs F7: 2,5 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0048-base-pr-000.dot * REASONING * DIS # B3: 5,8 => CTR => B3: 2,4 * CNT 1 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F2,G2,G3,H5,H7,I1) * ..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81. * PAIR F2: 4,5 BLK 2 E3: 4,5,8,9 # reduction candidate for 4,5 E3: 8,9 # 9 pairs E3: 4,5 # 9 pairs * PAIR F2: 4,5 ROW 2 A2: 4,5,7 # reduction candidate for 4,5 A2: 4,5 # 9 pairs A2: 7 # 7 pairs * PAIR I1: 7,8 BLK 3 I2: 7,8,1 # reduction candidate for 7,8 I2: 1 # 16 pairs I2: 7,8 # 7 pairs * PAIR I1: 7,8 ROW 1 B1: 7,8,2,4 # reduction candidate for 7,8 B1: 7,8 # 9 pairs B1: 2,4 # 7 pairs * PAIR G2: 1,4 COL G G4: 1,4,3,9 # reduction candidate for 1,4 G4: 1,4 # 10 pairs G4: 3,9 # 8 pairs * PAIR G3: 2,4 BLK 3 H1: 2,4,8 # reduction candidate for 2,4 H1: 8 # 16 pairs H1: 2,4 # 7 pairs * PAIR G3: 2,4 ROW 3 B3: 2,4,5,8 # reduction candidate for 2,4 B3: 5,8 => CTR * .26.1.5...3.26..9.1....7236..27...6.6..5.1..2.1..2675.89.1..624261..8.7...46.281. * PAIR RESTART * PAIR G3: 2,4 BLK 3 H1: 2,4,8 # reduction candidate for 2,4 H1: 8 => CTR * 926314587738265491145..723658274916.6..5.1.42.1..2675.89.153624261..8.75354672819 * PAIR H5: 4,8 BLK 6 H6: 4,8,5 # reduction candidate for 4,8 H6: 5 => CTR * .26.1.54..3.26419.14..57236.827...6167.5.1.82.1.82675.89.1.56242614.8.75.546.281. * PAIR H5: 4,8 ROW 5 B5: 4,8,7 # reduction candidate for 4,8 B5: 4,8 # 18 pairs E5: 4,8,3,9 # reduction candidate for 4,8 E5: 4,8 => CTR * 9.6.14527.3.26519.125..74365.27...6167.5.1..2.1..267.5897132654361458279254679813 * RESTART * PAIR H5: 4,8 ROW 5 B5: 4,8,7 # reduction candidate for 4,8 B5: 7 => CTR * ..6.1.52..3.26.19.12...7436..27...616785.1.42.1..26785897132654361.5827925467.81. * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,B1,B5,C2,C6,D3,D8,E3,E5,F2,G4,G5,H5,H6,I1,I2,I8,I9) * ..6.1.52..3.26.19.12...7436.5278..616.75.1..2.1..267.5893172654561.4827.2746..81. * PAIR B1: 4,8 ROW 1 D1: 4,8,3,9 # reduction candidate for 4,8 D1: 4,8 => SOLVED * 946813527735264198128957436452789361687531942319426785893172654561348279274695813 * DURATION: 0:00:20.182836 START: 04:23:19.557515 END: 04:23:39.740351 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0048-base-pr-001.dot * REASONING * DIS # B3: 5,8 => CTR => B3: 2,4 * DIS B3: 2,4 # H1: 8 => CTR => H1: 2,4 * DIS B3: 2,4 + H1: 2,4 # H6: 5 => CTR => H6: 4,8 * DIS B3: 2,4 + H1: 2,4 + H6: 4,8 # E5: 4,8 => CTR => E5: 3,9 * DIS B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 7 => CTR => B5: 4,8 * PRF B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 # D1: 4,8 => SOL * STA B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 + D1: 4,8 * CNT 6 HDP CHAINS / 23 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=48
Solution
position: 946813527735264198128957436452789361687531942319426785893172654561348279274695813 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* INC # E3: 4,5 => UNS * INC # E3: 8,9 => UNS * INC # A2: 4,5 => UNS * INC # A2: 7 => UNS * INC # I2: 7,8 => UNS * INC # I2: 1 => UNS * INC # B1: 7,8 => UNS * INC # B1: 2,4 => UNS * INC # G4: 1,4 => UNS * INC # G4: 3,9 => UNS * INC # H1: 2,4 => UNS * INC # H1: 8 => UNS * INC # B3: 2,4 => UNS * DIS # B3: 5,8 => CTR => B3: 2,4 * INC # H6: 4,8 => UNS * INC # H6: 5 => UNS * INC # B5: 4,8 => UNS * INC # E5: 4,8 => UNS * INC # H1: 4,8 => UNS * INC # H1: 2 => UNS * INC # F7: 2,5 => UNS * INC # F7: 3 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E3: 4,5 => UNS * INC # E3: 8,9 => UNS * INC # A2: 4,5 => UNS * INC # A2: 7 => UNS * INC # I2: 7,8 => UNS * INC # I2: 1 => UNS * INC # B1: 7,8 => UNS * INC # B1: 2,4 => UNS * INC # G4: 1,4 => UNS * INC # G4: 3,9 => UNS * INC # H1: 2,4 => UNS * INC # H1: 8 => UNS * INC # B3: 2,4 => UNS * DIS # B3: 5,8 => CTR => B3: 2,4 * INC B3: 2,4 # H1: 2,4 => UNS * DIS B3: 2,4 # H1: 8 => CTR => H1: 2,4 * INC B3: 2,4 + H1: 2,4 # H6: 4,8 => UNS * DIS B3: 2,4 + H1: 2,4 # H6: 5 => CTR => H6: 4,8 * INC B3: 2,4 + H1: 2,4 + H6: 4,8 # B5: 4,8 => UNS * DIS B3: 2,4 + H1: 2,4 + H6: 4,8 # E5: 4,8 => CTR => E5: 3,9 * INC B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 4,8 => UNS * DIS B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 7 => CTR => B5: 4,8 * PRF B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 # D1: 4,8 => SOL * STA B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 + D1: 4,8 * CNT 23 HDP CHAINS / 23 HYP OPENED